Question

a triangle has sides with lengths of 87 millimeters, 20 millimeters, and 84 millimeters. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse, the longest side), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 20\), \(b = 84\), and \(c = 87\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=20^{2}+84^{2}=400 + 7056=7456\).

Step3: Calculate \(c^{2}\)

\(c^{2}=87^{2}=7569\).

Step4: Compare

Since \(7456
eq7569\), i.e., \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no